Finite Group Databasebeta

← C2×#23777017 #35195361

Subgroups — C2×#23777017 #35195361

Order 20224.

7706 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777017C2132yesmaximal, direct product factor
2C2×#19099289C211yesmaximal, characteristic, complemented
3C2×#19099285C213yesmaximal, complemented
4C2×#19099254C213yesmaximal, complemented
5C2×#19099248C213yesmaximal, complemented
6C2×Q8×C22⋊D79C211yesmaximal, characteristic, complemented
7C2×#19099225C211yesmaximal, characteristic, complemented
8C2×#19099224C211yesmaximal, characteristic, complemented
9C2×#19099214C213yesmaximal, complemented
10C2×#19099117C213yesmaximal, complemented
11C2×#19099100C213yesmaximal, complemented
12C2×#19099097C213yesmaximal, complemented
13C2×C4×#11929625C211yesmaximal, characteristic, complemented
14C2×C4×#11929624C213yesmaximal, complemented
15C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C79C211yesmaximal, characteristic, complemented
17C22×#11929625C2211yescharacteristic
18C22×#11929624C2213yes—
19C22×Q8×D79C2211yescharacteristic
20#19099289C22116yescomplemented
21#19099285C22148yescomplemented
22#19099254C22148yescomplemented
23#19099248C22148yescomplemented
24Q8×C22⋊D79C22116yescomplemented
25#19099225C22116yescomplemented
26#19099224C22116yescomplemented
27#19099214C22148yescomplemented
28#19099117C22148yescomplemented
29C2×#14579160C2213yes—
30C2×#14579159C2213yes—
31#19099100C22148yescomplemented
32#19099097C22148yescomplemented
33C2×#14579156C2216yes—
34C2×#14579155C2216yes—
35C2×#14579153C2213yes—
36C2×#14579152C2213yes—
37C2×#14579151C2216yes—
38C2×#14579150C2213yes—
39C2×#14579149C2213yes—
40C2×#14579146C2216yes—
41C2×#14579144C2216yes—
42C2×#14579141C2213yes—
43C2×#14579140C2213yes—
44C2×#14579139C2216yes—
45C2×#14579137C2213yes—
46C2×#14579137C2213yes—
47C2×#14579136C2213yes—
48C2×#14579135C2213yes—
49C4×#11929625C22116yescomplemented
50C4×#11929624C22148yescomplemented
51C2×Q8×Dic79C2211yescharacteristic
52C2×Q8×Dic79C2211yescharacteristic
53C2×C4×Dic158C2213yes—
54C2×C4×Dic158C2213yes—
55C2×C4×Dic158C2213yes—
56C2×#14579126C2213yes—
57C4×Q8×D79C22116yescomplemented
58C2×C4×D316C2213yes—
59C2×C4×D316C2213yes—
60C2×C4×D316C2213yes—
61C2×#14579123C2213yes—
62C2×C4×C22⋊D79C2211yescharacteristic
63C2×C4×C22⋊D79C2213yes—
64C2×C4×C22⋊D79C2213yes—
65C2×C4×C22⋊D79C2213yes—
66C2×#14579120C2213yes—
67C2×#14579119C2213yes—
68C2×#14579118C2213yes—
69C2×#14579118C2213yes—
70C2×#14579118C2216yes—
71C2×C4⋊C4×D79C2213yes—
72C2×C42×D79C2213yes—
73C2×C42×D79C2213yes—
74C23×Q8×C79C2211yescharacteristic
75C2×C4×Q8×C79C2211yescharacteristic
76C2×C4×Q8×C79C2211yescharacteristic
77C2×C4×Q8×C79C2213yes—
78C2×C4×Q8×C79C2213yes—
79C2×C4×Q8×C79C22116yescomplemented
80C22×C4⋊C4×C79C2213yes—
81C22×C42×C79C2213yes—
82C2×#11929625—28no—
83C2×#11929625C2318yes—
84C2×#11929624—224no—
85C2×#11929624C23124yes—
86C22×Dic158C2313yes—
87C22×Dic158C2313yes—
88C2×Q8×D79—28no—
89C2×Q8×D79C2318yes—
90C22×D316C2313yes—
91C22×D316C2313yes—
92C22×C22⋊D79C2313yes—
93C22×C22⋊D79C2311yescharacteristic
94C22×C4×D79C2311yescharacteristic
95C22×C4×D79C2313yes—
96C22×C4×D79C2313yes—
97C22×C4×D79C2313yes—
98C22×C4×D79C2313yes—
99C22×C4×D79C2313yes—
100#14579160C23124yes—
101#14579159C23124yes—
102#14579156C23148yes—
103#14579155C23148yes—
104#14579153C23124yes—
105#14579152C23124yes—
106#14579151C23148yes—
107#14579150C23124yes—
108#14579149C23124yes—
109#14579146C23148yes—
110#14579144C23148yes—
111#14579141C23124yes—
112#14579140C23124yes—
113#14579139C23148yes—
114#14579137C23124yes—
115#14579137C23124yes—
116#14579136C23124yes—
117#14579135C23124yes—
118Q8×Dic79C2318yes—
119Q8×Dic79C2318yes—
120C4×Dic158C23124yes—
121C4×Dic158C23124yes—
122C4×Dic158C23124yes—
123#14579126C23124yes—
124C4×D316C23124yes—
125C4×D316C23124yes—
126C4×D316C23124yes—
127#14579123C23124yes—
128C4×C22⋊D79C23124yes—
129C4×C22⋊D79C23124yes—
130C4×C22⋊D79C2318yes—
131C4×C22⋊D79C23124yes—
132#14579120C23124yes—
133#14579119C23124yes—
134#14579118C23124yes—
135#14579118C23124yes—
136#14579118C23148yes—
137C2×C4⋊Dic79C2313yes—
138C2×C4⋊Dic79C2313yes—
139C2×C4⋊Dic79C2313yes—
140C2×C4⋊Dic79C2313yes—
141C2×Dic79⋊C4C2316yes—
142C2×Dic79⋊C4C2311yescharacteristic
143C2×Dic79⋊C4C2313yes—
144C2×Dic79⋊C4C2313yes—
145C2×Dic79⋊C4C2313yes—
146C2×Dic79⋊C4C2316yes—
147C2×Dic79⋊C4C2316yes—
148C4⋊C4×D79C23124yes—
149C2×C22⋊Dic79C2311yescharacteristic
150C2×C22⋊Dic79C2313yes—
151C2×(C2×D79)⋊C4C2311yescharacteristic
152C2×(C2×D79)⋊C4C2313yes—
153C2×(C2×D79)⋊C4C2313yes—
154C2×(C2×D79)⋊C4C2313yes—
155C2×(C2×D79)⋊C4C2316yes—
156C2×(C2×D79)⋊C4C2316yes—
157C2×(C2×D79)⋊C4C2316yes—
158C2×C4×Dic79C2311yescharacteristic
159C2×C4×Dic79C2313yes—
160C2×C4×Dic79C2313yes—
161C2×C4×Dic79C2313yes—
162C2×C4×Dic79C2313yes—
163C2×C4×Dic79C2313yes—
164C42×D79C23124yes—
165C42×D79C23124yes—
166C22×Q8×C79—28no—
167C22×Q8×C79C2318yes—
168C22×Q8×C79C2313yes—
169C22×Q8×C79C2311yescharacteristic
170C23×C4×C79C2311yescharacteristic
171C23×C4×C79C2313yes—
172C23×C4×C79C2313yes—
173C4×Q8×C79C2318yes—
174C4×Q8×C79C23124yes—
175C4×Q8×C79C2318yes—
176C4×Q8×C79C23124yes—
177C2×C4⋊C4×C79C23124yes—
178C2×C4⋊C4×C79C2313yes—
179C2×C4⋊C4×C79C2313yes—
180C2×C4⋊C4×C79C2316yes—
181C2×C42×C79C2313yes—
182C2×C42×C79C2313yes—
183C2×C42×C79C2313yes—
184C2×C42×C79C2313yes—
185C2×C42×C79C23124yes—
186C23×D79C2413yes—
187C23×D79C2411yescharacteristic
188#11929625—232no—
189#11929624—296no—
190C2×Dic158—212no—
191C2×Dic158—212no—
192C2×Dic158C24112yes—
193C2×Dic158C24112yes—
194Q8×D79—232no—
195C2×D316—212no—
196C2×D316—212no—
197C2×D316C24112yes—
198C2×D316C24112yes—
199C2×C22⋊D79—212no—
200C2×C22⋊D79#4118yescomplemented
201C2×C22⋊D79C24112yes—
202C2×C22⋊D79C2414yes—
203C22×Dic79C2413yes—
204C22×Dic79C2413yes—
205C22×Dic79C2411yescharacteristic
206C22×Dic79C2411yescharacteristic
207C22×Dic79C2413yes—
208C22×Dic79C2411yescharacteristic
209C2×C4×D79—212no—
210C2×C4×D79—212no—
211C2×C4×D79—212no—
212C2×C4×D79—212no—
213C2×C4×D79—24no—
214C2×C4×D79—212no—
215C2×C4×D79C24112yes—
216C2×C4×D79C24112yes—
217C2×C4×D79C24112yes—
218C2×C4×D79C24112yes—
219C2×C4×D79C2414yes—
220C2×C4×D79C24112yes—
221C4⋊Dic79C24112yes—
222C4⋊Dic79C24112yes—
223C4⋊Dic79C24112yes—
224C4⋊Dic79C24112yes—
225Dic79⋊C4C24124yes—
226Dic79⋊C4C2414yes—
227Dic79⋊C4C24112yes—
228Dic79⋊C4C24112yes—
229Dic79⋊C4C24112yes—
230Dic79⋊C4C24124yes—
231Dic79⋊C4C24124yes—
232C22⋊Dic79C2414yes—
233C22⋊Dic79C24112yes—
234(C2×D79)⋊C4C2414yes—
235(C2×D79)⋊C4C24112yes—
236(C2×D79)⋊C4C24112yes—
237(C2×D79)⋊C4C24112yes—
238(C2×D79)⋊C4C24124yes—
239(C2×D79)⋊C4C24124yes—
240(C2×D79)⋊C4C24124yes—
241C4×Dic79C2414yes—
242C4×Dic79C24112yes—
243C4×Dic79C24112yes—
244C4×Dic79C24112yes—
245C4×Dic79C24112yes—
246C4×Dic79C24112yes—
247C24×C79C2411yescharacteristic
248C2×Q8×C79—232no—
249C2×Q8×C79—212no—
250C2×Q8×C79#4118yescomplemented
251C2×Q8×C79C24112yes—
252C2×Q8×C79C2414yes—
253C22×C4×C79—212no—
254C22×C4×C79—212no—
255C22×C4×C79—24no—
256C22×C4×C79C2413yes—
257C22×C4×C79C24112yes—
258C22×C4×C79C2411yescharacteristic
259C22×C4×C79C2414yes—
260C22×C4×C79C2413yes—
261C22×C4×C79C2413yes—
262C22×C4×C79C24112yes—
263C22×C4×C79C2413yes—
264C22×C4×C79C2411yescharacteristic
265C4⋊C4×C79C24112yes—
266C4⋊C4×C79C24112yes—
267C4⋊C4×C79C24124yes—
268C42×C79C24112yes—
269C42×C79C24112yes—
270C42×C79C24112yes—
271C42×C79C24112yes—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79C2×#4114yes—
275C23×C79C2512yes—
276C23×C79C2511yescharacteristic
277C22×D79—22no—
278C22×D79—22no—
279C22×D79—26no—
280C22×D79—26no—
281C22×D79—26no—
282C22×D79C2×#4114yes—
283C22×D79C2516yes—
284C22×D79C2512yes—
285Q8×C79—224no—
286Q8×C79C2×#41116yescomplemented
287C2×C4×C79—26no—
288C2×C4×C79—26no—
289C2×C4×C79—224no—
290C2×C4×C79—26no—
291C2×C4×C79—22no—
292C2×C4×C79—224no—
293C2×C4×C79—28no—
294C2×C4×C79C2×#41112yes—
295C2×C4×C792−1+414yes—
296C2×C4×C79C2516yes—
297C2×C4×C79C2512yes—
298C2×C4×C79C2516yes—
299C2×C4×C79C2516yes—
300C2×C4×C79C2516yes—
301C2×C4×C79C2512yes—
302C22⋊D79—224no—
303C22⋊D79C2×#41116yescomplemented
304C2×Dic79—22no—
305C2×Dic79—26no—
306C2×Dic79—26no—
307C2×Dic79—22no—
308C2×Dic79—26no—
309C2×Dic79C2×#4114yes—
310C2×Dic79C2512yes—
311C2×Dic79C2512yes—
312C2×Dic79C2516yes—
313C2×Dic79C2516yes—
314C2×Dic79C2516yes—
315C2×Dic79C2512yes—
316D316—224no—
317D316—224no—
318C4×D79—224no—
319C4×D79—224no—
320C4×D79—224no—
321C4×D79—28no—
322C4×D79—224no—
323C4×D79—224no—
324Dic158—224no—
325Dic158—224no—
326C22×C79—22no—
327C22×C79—22no—
328C22×C79—28no—
329C22×C79C22×#4114yes—
330C22×C79C22×#4112yes—
331C22×C79C22×#4112yes—
332C22×C79C2×2−1+412yes—
333C22×C79C2611yescharacteristic
334C2×D79—22no—
335C2×D79—22no—
336C2×D79—28no—
337C2×D79—26no—
338C2×D79—26no—
339C2×D79—26no—
340C2×D79—412no—
341C2×D79C22×#4114yes—
342C4×C79—26no—
343C4×C79—26no—
344C4×C79—26no—
345C4×C79—22no—
346C4×C79C22×#41112yes—
347C4×C79C2×2−1+414yes—
348Dic79—26no—
349Dic79—26no—
350Dic79—22no—
351Dic79—22no—
352Dic79—26no—
353Dic79C22×#4114yes—
354C2×#3482—791nomaximal, Sylow
355C2×C79—24no—
356C2×C79#348214yescomplemented
357C2×C79C23×#4111yescharacteristic
358C2×C79C23×#4111yescharacteristic
359C2×C79C22×2−1+411yescharacteristic
360D79—24no—
361D79—46no—
362#3482—7932no—
363C2×#557—791no—
364C2×#556—793no—
365C2×#552—793no—
366C2×#552—793no—
367C2×D4×Q8—791no—
368C2×#548—791no—
369C2×#548—791no—
370C2×#547—793no—
371C2×#533—793no—
372C2×#529—793no—
373C2×#529—793no—
374C2×C4×#41—793no—
375C2×C4×#41—791no—
376C22×C4×Q8—791no—
377C22×C4×Q8D7911yescharacteristic, complemented
378C79C2×#348211yescharacteristic, complemented, Sylow
379C22×#41—791no—
380C22×#41—793no—
381C23×Q8—791no—
382C23×Q8C2×D7911yescharacteristic
383#557—7916no—
384#556—7948no—
385#552—7948no—
386#552—7948no—
387D4×Q8—7916no—
388#548—7916no—
389#548—7916no—
390#547—7948no—
391#533—7948no—
392C2×C4⋊Q8—793no—
393C2×C4⋊Q8—793no—
394#529—7948no—
395#529—7948no—
396C2×#126—796no—
397C2×#126—796no—
398C2×#125—793no—
399C2×#125—796no—
400C2×#125—793no—
401C2×#124—793no—
402C2×#124—793no—
403C2×#123—796no—
404C2×#123—796no—
405C2×C22⋊Q8—793no—
406C2×C22⋊Q8—793no—
407C2×C22⋊Q8—793no—
408C2×C22⋊Q8—796no—
409C2×C22⋊Q8—793no—
410C2×#121—793no—
411C2×#121—793no—
412C4×#41—7916no—
413C4×#41—7948no—
414C2×C4×Q8—791no—
415C2×C4×Q8—791no—
416C2×C4×Q8—7916no—
417C2×C4×Q8—793no—
418C2×C4×Q8—793no—
419C2×C4×Q8—793no—
420C2×C4×Q8—793no—
421C2×C4×Q8C2×D7911yescharacteristic
422C2×C4×Q8C2×D7913yes—
423C2×C4×Q8C2×D7911yescharacteristic
424C2×C4×Q8C2×D7913yes—
425C2×C4×Q8C2×D79116yescomplemented
426C2×C4×D4—791no—
427C2×C4×D4—793no—
428C2×C4×D4—793no—
429C2×C4×D4—793no—
430C2×C4×D4—793no—
431C2×C4×D4—793no—
432C2×C4×D4—793no—
433C2×C4×D4—793no—
434C2×#117—793no—
435C2×#117—793no—
436C2×#117—793no—
437C2×#117—793no—
438C2×#117—796no—
439C22×C4⋊C4—793no—
440C22×C4⋊C4C2×D7913yes—
441C22×C42—793no—
442C22×C42—793no—
443C22×C42C2×D7913yes—
444C2×#41—798no—
445C2×#41—7924no—
446C2×#41—15824no—
447C2×#41—1588no—
448C22×Q8—28no—
449C22×Q8—798no—
450C22×Q8—793no—
451C22×Q8—793no—
452C22×Q8—1588no—
453C22×Q8C22×D7913yes—
454C22×Q8C22×D7918yes—
455C22×Q8C22×D7911yescharacteristic
456C22×D4—791no—
457C22×D4—793no—
458C22×D4—793no—
459C22×D4—793no—
460C23×C4—793no—
461C23×C4—793no—
462C23×C4—793no—
463C23×C4—793no—
464C23×C4—793no—
465C23×C4—791no—
466C23×C4C22×D7913yes—
467C23×C4C22×D7913yes—
468C23×C4C22×D7911yescharacteristic
469C4⋊Q8—7924no—
470C4⋊Q8—7924no—
471#126—7948no—
472#126—7948no—
473#125—7924no—
474#125—7948no—
475#125—7924no—
476#124—7924no—
477#124—7924no—
478#123—7948no—
479#123—7948no—
480C22⋊Q8—7924no—
481C22⋊Q8—7924no—
482C22⋊Q8—7924no—
483C22⋊Q8—7948no—
484C22⋊Q8—7924no—
485#121—7924no—
486#121—7924no—
487C4×Q8—798no—
488C4×Q8—798no—
489C4×Q8—7924no—
490C4×Q8—7924no—
491C4×Q8—7924no—
492C4×Q8—7924no—
493C4×Q8C22×D7918yes—
494C4×Q8C22×D79124yes—
495C4×Q8C22×D7918yes—
496C4×Q8C22×D79124yes—
497C4×D4—798no—
498C4×D4—7924no—
499C4×D4—7924no—
500C4×D4—7924no—
501C4×D4—7924no—
502C4×D4—7924no—
503C4×D4—7924no—
504C4×D4—7924no—
505#117—7924no—
506#117—7924no—
507#117—7924no—
508#117—7924no—
509#117—7948no—
510C2×C4⋊C4—793no—
511C2×C4⋊C4—796no—
512C2×C4⋊C4—791no—
513C2×C4⋊C4—793no—
514C2×C4⋊C4—793no—
515C2×C4⋊C4—793no—
516C2×C4⋊C4—793no—
517C2×C4⋊C4—793no—
518C2×C4⋊C4—793no—
519C2×C4⋊C4—796no—
520C2×C4⋊C4—796no—
521C2×C4⋊C4—7924no—
522C2×C4⋊C4C22×D7913yes—
523C2×C4⋊C4C22×D7913yes—
524C2×C4⋊C4C22×D7916yes—
525C2×C4⋊C4C22×D79124yes—
526C2×C22⋊C4—791no—
527C2×C22⋊C4—793no—
528C2×C22⋊C4—791no—
529C2×C22⋊C4—793no—
530C2×C22⋊C4—796no—
531C2×C22⋊C4—793no—
532C2×C22⋊C4—793no—
533C2×C22⋊C4—796no—
534C2×C22⋊C4—796no—
535C2×C42—793no—
536C2×C42—793no—
537C2×C42—793no—
538C2×C42—793no—
539C2×C42—793no—
540C2×C42—791no—
541C2×C42—7924no—
542C2×C42—7924no—
543C2×C42C22×D7913yes—
544C2×C42C22×D7913yes—
545C2×C42C22×D79124yes—
546C2×C42C22×D7913yes—
547C2×C42C22×D7913yes—
548C24—791no—
549C24—793no—
550C24C23×D7911yescharacteristic
551#41—15896no—
552#41—15832no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—7912no—
556C2×Q8—7912no—
557C2×Q8—15812no—
558C2×Q8—15832no—
559C2×Q8—15812no—
560C2×Q8#1192962418yescomplemented
561C2×Q8C23×D79112yes—
562C2×Q8C23×D7914yes—
563C2×D4—798no—
564C2×D4—794no—
565C2×D4—7912no—
566C2×D4—7912no—
567C2×D4—7912no—
568C2×D4—15812no—
569C2×D4—15812no—
570C2×D4—15812no—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—24no—
574C22×C4—791no—
575C22×C4—791no—
576C22×C4—791no—
577C22×C4—793no—
578C22×C4—793no—
579C22×C4—793no—
580C22×C4—794no—
581C22×C4—7912no—
582C22×C4—7912no—
583C22×C4—7912no—
584C22×C4—7912no—
585C22×C4—7912no—
586C22×C4—15812no—
587C22×C4—15812no—
588C22×C4—15812no—
589C22×C4—15812no—
590C22×C4—15812no—
591C22×C4—1584no—
592C22×C4C23×D7913yes—
593C22×C4C23×D7911yescharacteristic
594C22×C4C23×D7914yes—
595C22×C4C23×D7913yes—
596C22×C4C23×D7913yes—
597C22×C4C23×D79112yes—
598C22×C4C23×D79112yes—
599C22×C4C23×D7913yes—
600C22×C4C23×D7911yescharacteristic
601C4⋊C4—7924no—
602C4⋊C4—794no—
603C4⋊C4—7912no—
604C4⋊C4—7912no—
605C4⋊C4—7912no—
606C4⋊C4—7924no—
607C4⋊C4—7924no—
608C4⋊C4—7912no—
609C4⋊C4—7912no—
610C4⋊C4—7912no—
611C4⋊C4—7912no—
612C4⋊C4C23×D79112yes—
613C4⋊C4C23×D79112yes—
614C4⋊C4C23×D79124yes—
615C22⋊C4—794no—
616C22⋊C4—7912no—
617C22⋊C4—794no—
618C22⋊C4—7912no—
619C22⋊C4—7924no—
620C22⋊C4—7912no—
621C22⋊C4—7912no—
622C22⋊C4—7924no—
623C22⋊C4—7924no—
624C42—794no—
625C42—7912no—
626C42—7912no—
627C42—7912no—
628C42—7912no—
629C42—7912no—
630C42C23×D79112yes—
631C42C23×D79112yes—
632C42C23×D79112yes—
633C42C23×D79112yes—
634C23—22no—
635C23—22no—
636C23—792no—
637C23—794no—
638C23—796no—
639C23—1586no—
640C23—1586no—
641C23—1586no—
642C23—1582no—
643C23—1582no—
644C23#41×D7914yes—
645C23C24×D7912yes—
646C23C24×D7911yescharacteristic
647Q8—224no—
648Q8—15824no—
649Q8—15824no—
650Q8C2×#11929624116yescomplemented
651D4—7916no—
652D4—15824no—
653D4—15824no—
654D4—15824no—
655C2×C4—22no—
656C2×C4—26no—
657C2×C4—26no—
658C2×C4—224no—
659C2×C4—26no—
660C2×C4—28no—
661C2×C4—224no—
662C2×C4—792no—
663C2×C4—794no—
664C2×C4—792no—
665C2×C4—792no—
666C2×C4—796no—
667C2×C4—796no—
668C2×C4—796no—
669C2×C4—15824no—
670C2×C4—15824no—
671C2×C4—1582no—
672C2×C4—1586no—
673C2×C4—1586no—
674C2×C4—1582no—
675C2×C4—1586no—
676C2×C4—15824no—
677C2×C4—1588no—
678C2×C4—15824no—
679C2×C4—15824no—
680C2×C4C2×#11929624112yes—
681C2×C4#1457920914yes—
682C2×C4C24×D7916yes—
683C2×C4C24×D7912yes—
684C2×C4C24×D7916yes—
685C2×C4C24×D7916yes—
686C2×C4C24×D7912yes—
687C2×C4C24×D7916yes—
688C22—22no—
689C22—22no—
690C22—28no—
691C22—31612no—
692C22—794no—
693C22—1586no—
694C22—1586no—
695C22—1586no—
696C22—1582no—
697C22—1582no—
698C22—1588no—
699C22C2×#41×D7914yes—
700C22C2×#41×D7912yes—
701C22C22×#1192962412yes—
702C22C2×#1457920912yes—
703C22C25×D7911yescharacteristic
704C4—26no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—794no—
709C4—1586no—
710C4—1582no—
711C4—1586no—
712C4—1582no—
713C4—1586no—
714C4C22×#11929624112yes—
715C4C2×#1457920914yes—
716C2—24no—
717C2—3166no—
718C2—1584no—
719C2#2377701714yesdirect product factor
720C2C22×#41×D7911yescharacteristic
721C2C23×#1192962411yescharacteristic
722C2C22×#1457920911yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC22×C4×Q8×C79C2
socleC23×C79C25
hypercenterC22×C4×Q8D79
hypocenterC79C2×#3482
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777017C2direct (N × H)
2. C2×#19099289C2semidirect
3. C2×#19099285C2semidirect
4. C2×#19099254C2semidirect
5. C2×#19099248C2semidirect
6. C2×Q8×C22⋊D79C2semidirect
7. C2×#19099225C2semidirect
8. C2×#19099224C2semidirect
9. C2×#19099214C2semidirect
10. C2×#19099117C2semidirect
11. C2×#19099100C2semidirect
12. C2×#19099097C2semidirect
13. C2×C4×#11929625C2semidirect
14. C2×C4×#11929624C2semidirect
15. C2×C4×Q8×D79C2semidirect
16. C22×C4×Q8×C79C2semidirect
20. #19099289C22semidirect
21. #19099285C22semidirect
22. #19099254C22semidirect
23. #19099248C22semidirect
24. Q8×C22⋊D79C22semidirect
25. #19099225C22semidirect
26. #19099224C22semidirect
27. #19099214C22semidirect
28. #19099117C22semidirect
31. #19099100C22semidirect
32. #19099097C22semidirect
49. C4×#11929625C22semidirect
50. C4×#11929624C22semidirect
57. C4×Q8×D79C22semidirect
79. C2×C4×Q8×C79C22semidirect
200. C2×C22⋊D79#41semidirect
250. C2×Q8×C79#41semidirect
286. Q8×C79C2×#41semidirect
303. C22⋊D79C2×#41semidirect
356. C2×C79#3482semidirect
377. C22×C4×Q8D79semidirect
378. C79C2×#3482semidirect
425. C2×C4×Q8C2×D79semidirect
560. C2×Q8#11929624semidirect
650. Q8C2×#11929624semidirect
719. C2#23777017direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237770172
C2×#190992892
C2×#190992852
C2×#190992542
C2×#190992482
C2×Q8×C22⋊D792
C2×#190992252
C2×#190992242
C2×#190992142
C2×#190991172
C2×#190991002
C2×#190990972
C2×C4×#119296252
C2×C4×#119296242
C2×C4×Q8×D792
C22×C4×Q8×C792
C2×#348279